Conventional mooring systems for Mobile Offshore Drilling Units (MODU), Floating Production Storage & Offloading (FPSO) and Floating Storage & Offloading (FSO) vessels rely on pre-tensioning of their respective mooring lines by means of winches, windlasses or chain jacks mounted on the vessel itself. Mounting of mooring line tensioning equipment on the deck of a vessel is generally not a problem for a MODU or a FPSO or FSO that is equipped with a spread mooring. However, deck-mounting of tensioning equipment may be difficult or impossible under some circumstances, such as when a MODU needs to add additional mooring legs (e.g., for compliance with requirements by the Bureau of Safety and Environmental Enforcement (BSEE) for drilling in the Gulf of Mexico during the hurricane season), and when a FPSO or FSO is equipped with an internal or external turret mooring system. For example, in the case of a MODU originally designed for eight mooring legs, but that now requires twelve mooring legs, it is often difficult to accommodate four more tensioning systems and associated chain lockers required for the four additional legs. In the case of a FPSO or FPO with a turret mooring system, it is very difficult to mount mooring tensioning equipment on the turret due to lack of space.